• Steel and Composite Structures
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• v.19 no.3
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• pp.521-546
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• 2015

A new refined hyperbolic shear and normal deformation beam theory is developed to study the free vibration and buckling of functionally graded (FG) sandwich beams under various boundary conditions. The effects of transverse shear strains as well as the transverse normal strain are taken into account. Material properties of the sandwich beam faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending, free vibration and buckling analyses are obtained for simply supported sandwich beams. Illustrative examples are given to show the effects of varying gradients, thickness stretching, boundary conditions, and thickness to length ratios on the bending, free vibration and buckling of functionally graded sandwich beams.

• Journal of Ship and Ocean Technology
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• v.4 no.2
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• pp.38-57
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• 2000

This paper deals with reliability analysis of specially orthotropic plates subjected to transverse lateral pressure loads by using Monte Carlo simulation method. The plates are simply supported around their all edges and have a low short span to plate depth ratio with rectangular plate shapes. Various levels of reliability analyses of the plates are performed within the context of First-Ply-Failure(FPF) analysis such as ply-/laminate-level reliability analyse, failure tree analysis and sensitivity analysis of basic design variables to estimated plate reliabilities. In performing all these levels of reliability analyses, the followings are considered within the Monte Carlo simulation method: (1) input parameters to the strengths of the plates such as applied transverse lateral pressure loads, elastic moduli, geometric including plate thickness and ultimate strength values of the plates are treated as basic design variables following a normal probability distribution; (2) the mechanical responses of the plates are calculated by using simplified higher-order shear deformation theory which can predict the mechanical responses of thick laminated plates accurately; and (3) the limit state equations are derived from polynomial failure criteria for composite materials such as maximum stress, maximum strain, Tsai-Hill, Tsai-Wu and Hoffman.

• Earthquakes and Structures
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• v.7 no.5
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• pp.843-859
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• 2014

In the present study, the seismic performance of structural walls with boundary elements confined by conventional tie hoops and steel fiber concrete (SFC) was investigated. Cyclic lateral loading tests on four wall specimens under constant axial load were performed. The primary test parameters considered were the spacing of boundary element transverse reinforcement and the use of steel fiber concrete. Test results showed that the wall specimen with boundary elements complying with ACI 318-11 21.9.6 failed at a high drift ratio of 4.5% due to concrete crushing and re-bar buckling. For the specimens where SFC was selectively used in the plastic hinge region, the spalling and crushing of concrete were substantially alleviated. However, sliding shear failure occurred at the interface of SFC and plain concrete at a moderate drift ratio of 3.0% as tensile plastic strains of longitudinal bars were accumulated during cyclic loading. The behaviors of wall specimens were examined through nonlinear section analysis adopting the stress-strain relationships of confined concrete and SFC.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.14 no.11
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• pp.892-897
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• 2001

Variations of dielectric and piezoelectric properties and associated phase transformation of <001> -oriented rhombohedral 0.92Pb (Zn$\sub$1/3/Nb$\sub$2/3/)O$_3$-0.08PbTiO$_3$ single crystals were investigated. The longitudinal strain level was found to abruptly increase at 15 kV/cm, corresponding to that where an induced phase appears within a multidomain matrix. Drastic decreases in the dielectric constant, transverse coupling, and transverse piezoelectric coefficient associated with the E-field induced phase were the result of increased crystal anisotropy in PZN-PT crystals. By contrast, the thickness coupling increased from 53 % at 0 kV/cm to 64 % at 45 kV/cm, also associated with this phase transition under the E-field. The measured dielectric and piezflelectric properties found for the induced phase state were nearly identical to those of <001> poled tetragonal (1-x)PZN-xPT (x>0.1) crystals. Based on these results, it is evident that the symmetry of induced phase is tetragonal.

• Advances in materials Research
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• v.5 no.2
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• pp.107-120
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• 2016

The static analysis of the simply supported functionally graded plate under transverse load by using a new sinusoidal shear deformation theory based on the neutral surface concept is investigated analytically in the present paper. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. The mechanical properties of the FGM plate are assumed to vary continuously through the thickness according to a power law formulation except Poisson's ratio, which is kept constant. The equilibrium and stability equations are derived by employing the principle of virtual work. Results are provided for thick to thin plates and for different values of the gradient index k, which subjected to sinusoidal or uniformly distributed lateral loads. The accuracy of the present results is verified by comparing it with finite element solution. From the obtained results, it can be concluded that the proposed theory is accurate and efficient in predicting the displacements and stresses of functionally graded plates.

• Steel and Composite Structures
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• v.42 no.1
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• pp.75-90
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• 2022

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.

• Journal of Korean Society of Steel Construction
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• v.16 no.4 s.71
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• pp.493-500
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• 2004

In this study, the effects of ring stiffeners for buckling of cylindrical shells with composite materials were analyzed. The finite element method was used: 3-D beam elements were used for stiffeners and flat shell elements were used for cylindrical shells and were improved by introducing a substitute shear strain. The ring stiffeners were of the transverse rib type. The buckling behaviors of the cylindrical shells were analyzed based on various parameters, such as locations and sizes of stiffeners, diameter/length ratios and boundary conditions of shells, and fiber-reinforced angles. Effective reinforcement was examined by understanding the exact behaviors for buckling. The results of the analysis may serve as references for designs and future investigations.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.1-12
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• 2002

To obtain more accurate responses of laminated composite structures, the effect of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane displacements with respect to the thickness coordinate need to be considered in the analysis. The improved higher-order theory is used to determine the deflections and natural frequencies of laminated composite structures. A quasi-elastic method is used for the solution of viscoelastic analysis of the laminated composite plates and sandwiches. Solutions of simply-supported laminated composite plates and sandwiches are obtained and the results are compared with those by the 3D elasticity theory and other theories. The improved theory proposed in this paper is shown to predict the deflections and natural frequencies more accurately than all other theories.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.227-241
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• 2020

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C⁰ finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.